value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Differentiate quotient rule functions, Example of quotient rule : Let's no...

Example of quotient rule : Let's now see example on quotient rule.  In this, unlike the product rule examples, some of these functions will require the quotient rule to get the de

Differential equation, Find the normalized differential equation which has ...

Find the normalized differential equation which has {x, xex} as its fundamental set

Right- and left-handed limits , Right- and left-handed limits : Next, let'...

Right- and left-handed limits : Next, let's see precise definitions for the right- & left-handed limits. Definition   For the right-hand limit we say that, if for eve

Implicit differentiation, Implicit Differentiation : To this instance w...

Implicit Differentiation : To this instance we've done quite a few derivatives, however they have all been derivatives of function of the form y = f ( x ) .  Unluckily not all

Example of factoring quadratic polynomials, Factor following polynomials. ...

Factor following polynomials.                               x 2 + 2x -15 Solution x 2 +2x -15 Okay since the first term is x 2 we know that the factoring has to ta

Conclude the values of the six trigonometric functions, Conclude the values...

Conclude the values of the six trigonometric functions: Conclude the values of the six trigonometric functions of an angle formed through the x-axis and a line connecting the

lmc, what is the concept of lm

what is the concept of lmc

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd